Sunday, 18 May 2014

Non-Deductive & Deductive Arguments

Deductive reasoning forms, if they are correctly formulated, can't be defeated. In that sense, they are like larger scale versions of analytical statements. That is, they're guaranteed to be true and correct. Induction, on the other hand, is defeasible. It's defeasible because the possibility is always left open that “new knowledge” may come along and defeat either the premises or the conclusion (or both). With deductive arguments, on the other hand, new knowledge would be irrelevant. Nothing could possibly invalidate a deductive conclusion if the way to that conclusion correctly followed the rules and forms of accepted deductive logic.

Flach gives as an example of non-deductive, therefore defeasible, logic this:

Birds typically fly.

Tweety is a bird.

Therefore Tweety flies.

I assume that this is a non-deductive argument quite simply because in the initial premise we have the word “typically”. That would make it a non-categorical statement. Therefore quite clearly it's defeasible. Though surely it could still be taken as a deductive argument simply by taking out the word “typically”. That is, this argument clearly leaves the possibility that there are certain non-typical birds. And if they aren't typical birds, then such birds may not in fact fly.

The first premise is effectively an inductive generalisation about birds. And if we call it a “generalisation”, then evidently there may well be exceptions to this rule.

For example, that two plus two equals four couldn't be deemed a generalisation of any kind. It is, however, a “plausible” piece of reasoning. That is, if it is indeed the case that birds typically fly, then there's a good chance that if Tweety is a bird, that Tweety can fly. However, because of the qualified first premise which implies that it's not logically necessary that it flies because that very premise left the possibility open that there are birds that can't fly. It's that qualificatory premise that really makes the above argument a non-deductive argument.

In these non-deductive inductive arguments, we need to distinguish whether or not it's the conclusion that can be defeated, or the premises (or both).

For example

Everyday during my life the sun rose.

I don’t know of any trustworthy report of the sun not rising one day in the past.

Therefore, the sun will rise every future day.

This too is a qualified argument based on a qualified initial premise. That is, it doesn't say that the sun must rise everyday. It simply says that the sun has risen everyday. This simply means that it leaves open the possibility that there could be an occasion in which the sun doesn't rise. Indeed it is that which makes it a non-deductive argument

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